Localization on quantum graphs with random edge lengths - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Letters in Mathematical Physics Année : 2009

Localization on quantum graphs with random edge lengths

Résumé

The spectral properties of the Laplacian on a class of quantum graphs with random metric structure are studied. Namely, we consider quantum graphs spanned by the simple $\ZZ^d$-lattice with $\delta$-type boundary conditions at the vertices, and we assume that the edge lengths are randomly independently identically distributed. Under the assumption that the coupling constant at the vertices does not vanish, we show that the operator exhibits the Anderson localization at the bottom of the spectrum almost surely. We also study the case of other spectral edges.
Fichier principal
Vignette du fichier
var13.pdf (193.23 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-00326964 , version 1 (06-10-2008)
hal-00326964 , version 2 (14-01-2009)

Identifiants

Citer

Frédéric Klopp, Konstantin Pankrashkin. Localization on quantum graphs with random edge lengths. Letters in Mathematical Physics, 2009, 87, pp.99-114. ⟨10.1007/s11005-009-0293-8⟩. ⟨hal-00326964v2⟩
144 Consultations
163 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More